R Dataset / Package HistData / Cavendish
On this Rdata statistics page, you will find information about the Cavendish data set which pertains to Cavendish's Determinations of the Density of the Earth. The Cavendish data set is found in the HistData R package. You can load the Cavendish data set in R by issuing the following command at the console data("Cavendish"). This will load the data into a variable called Cavendish. If R says the Cavendish data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data with the library() command. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Cavendish R data set. The size of this file is about 447 bytes.
Cavendish's Determinations of the Density of the Earth
Description
Henry Cavendish carried out a series of experiments in 1798 to determine the mean density of the earth, as an indirect means to calculate the gravitational constant, G, in Newton's formula for the force (f) of gravitational attraction, f = G m M / r^2 between two bodies of mass m and M.
Stigler (1977) used these data to illustrate properties of robust estimators with real, historical data. For these data sets, he found that trimmed means performed as well or better than more elaborate robust estimators.
Usage
data(Cavendish)
Format
A data frame with 29 observations on the following 3 variables.
density

Cavendish's 29 determinations of the mean density of the earth
density2

same as
density
, with the third value (4.88) replaced by 5.88 density3

same as
density
, omitting the the first 6 observations
Details
Density values (D) of the earth are given as relative to that of water. If the earth is regarded as a sphere of radius R, Newton's law can be expressed as G D = 3 g / (4 π R), where g=9.806 m/s^2 is the acceleration due to gravity; so G is proportional to 1/D.
density
contains Cavendish's measurements as analyzed, where he treated the value 4.88 as if it were 5.88. density2
corrects this. Cavendish also changed his experimental apparatus after the sixth determination, using a stiffer wire in the torsion balance. density3
replaces the first 6 values with NA
.
The modern "true" value of D is taken as 5.517. The gravitational constant can be expressed as G = 6.674 * 10^11 m^3/kg/s^2.
Source
Kyle Siegrist, "Virtual Laboratories in Probability and Statistics", http://www.math.uah.edu/stat/data/Cavendish.html
Stephen M. Stigler (1977), "Do robust estimators work with real data?", Annals of Statistics, 5, 10551098
References
Cavendish, H. (1798). Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, 88 (Part II), 469527. Reprinted in A. S. Mackenzie (ed.), The Laws of Gravitation, 1900, New York: American.
Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering, NY: Wiley, p. 520.
Examples
data(Cavendish) summary(Cavendish) boxplot(Cavendish, ylab='Density', xlab='Data set') abline(h=5.517, col="red", lwd=2)# trimmed means sapply(Cavendish, mean, trim=.1, na.rm=TRUE)# express in terms of G G < function(D, g=9.806, R=6371) 3*g / (4 * pi * R * D) boxplot(10^5 * G(Cavendish), ylab='~ Gravitational constant (G)', xlab='Data set') abline(h=10^5 * G(5.517), col="red", lwd=2)
Dataset imported from https://www.rproject.org.